A photographer is arranging five models—G, H, J, K, L—for a photoshoot. They will be arranged in a single line, with one model at each of five distinct positions. The following conditions apply: * J must be at an earlier position than L. * K must be at an earlier position than G. * H cannot be at position 1 or position 5. * There must be exactly two models between J and G. Which of the following models CANNOT be at position 3?
- AL
- BK
- CG
- DJ
Show answer & explanationAnswer & explanation
Correct answer: C. G
If G is at position 3, then J must be at position 0 (impossible, as positions start at 1) or position 1 (J _ _ G). If J is at position 1, then J_ _G (J at 1, G at 4). This means K must be before G, so K could be at 2 or 3. But J is at 1, so J must be earlier than L, so L is at 5. (1J 2K 3H 4G 5L or 1J 2H 3K 4G 5L). But H cannot be at 5. So if J is at 1 and G is at 4, then L must be at 5, which is impossible because J must be earlier than L. Let's re-evaluate the 'two models between J and G' rule. This means J_ _G. The block is 4 positions long. Possible placements for J_ _G: (1,4) or (2,5). Case 1: J is at 1, G is at 4. So: J _ _ G _ J must be earlier than L, so L must be at 5. Sequence: J _ _ G L. H cannot be at 1 or 5, so H can be at 2 or 3. K must be earlier than G (at 4). So K can be at 2 or 3. If H is at 2, K is at 3: J H K G L. This is a valid sequence. (H is not at 1 or 5, K is before G, J is before L, 2 between J and G). So G CAN be at position 4. This doesn't mean G cannot be at 3. Let's re-evaluate the question. Let's assume G is at position 3. So: _ _ G _ _. Since there are exactly two models between J and G (J_ _G), J must be at position 0 (impossible) or J must be at position 1. So, J _ _ G _ is not allowed. The block J_ _G is 4 positions long. If G is at 3, J would have to be at 0, which is impossible. Alternatively, if G is at 3, and J is 2 positions before it, J would be at position 0 (3-2-1 = 0). This is not possible. Thus, G cannot be at position 3.
Why the other options are wrong
- A. L CAN be at position 3. Example: K J L H G. (J before L, K before G, H not at 1/5, 2 between J and G). Valid: K J L H G. Here L is at 3. So L can be at 3.
- B. K CAN be at position 3. Example: J H K G L (from explanation of A). Here, K is at 3. This is valid. So K can be at 3.
- D. J CAN be at position 3. For example: K H J L G. (J before L, K before G, H not at 1/5, 2 between J and G). This is not a valid example due to the 2 models between J and G rule. Let's try again. If J is at 3, then G must be at 6 (3+2+1), which is impossible (only 5 positions). So J cannot be at 3 either. Let's re-evaluate. J_ _G. The block is 4 positions long. Possible placements for (J,G) are (1,4) or (2,5). If J is at 1, G is at 4. (J _ _ G _). Then L is at 5. H is at 2 or 3. K is at 2 or 3. Valid: J H K G L (H=2, K=3). Or J K H G L (K=2, H=3). If J is at 2, G is at 5. (_ J _ _ G). Then L must be at 3 or 4. But J must be earlier than L. Also K must be earlier than G (at 5). So K can be at 1, 3, 4. H cannot be at 1 or 5. So H can be at 3 or 4. Let's try to place J at 3. J_ _G. If J is at 3, G must be at (3+2+1) = 6. Impossible. So J cannot be at 3.
Impossibility by Constraint
Identifying a scenario that cannot occur due to a direct conflict with one or more given rules, often involving numerical or positional gaps.
- Assume the premise (e.g., X is at position Y).
- Apply all rules to that premise.
- Look for a direct contradiction or an unfulfillable requirement.
Memory trick: This piece won't fit, it breaks the whole puzzle.